Analysis of Peak Offensive Age in MLB Hitters

I. Abstract and Research Topic Introduction

(2 min read)

1.1Research Topic Introduction:

This study uses the historical Lahman Baseball Database to analyze the differences in peak offensive age (measured by OPS) among MLB players at different fielding positions. By comparing the peak ages of players across positions, we examine whether certain positions tend to reach their offensive prime earlier or later.
We also further investigate whether height and weight are associated with peak age and peak OPS, aiming to understand offensive characteristics across different positions.

1.2 Database Introduction:

The Lahman Database, created by Sean Lahman, contains comprehensive MLB statistics from 1871 to the present (current version includes data up to 2023). The database consists of many tables; for this study, the main tables used are:

Table Name	Description
Batting	Includes batting statistics such as hits, home runs, RBIs, etc.
People	Includes player information such as name, birthdate, and physical data.
Appearances	Includes information on player fielding positions.

Example Shohei Ohtani: ### tabset {.tabset} #### People

People |>
  filter(playerID == "ohtansh01")

Batting

Batting |>
  filter(playerID == "ohtansh01") |>  
  head(10)

Appearances

Appearances |>
  filter(playerID == "ohtansh01")

1.3 Metrics:

To evaluate offensive performance, we adopt On-base Plus Slugging (OPS) as the primary indicator. Before calculating OPS, we briefly introduce its components:

On-base Percentage (OBP):
Probability of reaching base per plate appearance.
\[ OBP = \frac{H + BB + HBP}{AB + BB + HBP + SF} \]

(H = Hits, BB = Walks, HBP = Hit By Pitch, AB = At Bats, SF = Sacrifice Flies)）
Slugging Percentage (SLG):
Average bases gained per at-bat.
\[ SLG = \frac{TB}{AB} \]

(TB = Total Bases, AB = At Bats)
(Single = 1 base, Double = 2 bases, Triple = 3 bases, Home Run = 4 bases)
On-base Plus Slugging (OPS):
Measures the overall offensive contribution of a hitter. As the name suggests, it is the sum of OBP and SLG.
\[ OPS = OBP + SLG \]

1.4 Fielding Position Introduction:

(You may skip this section if already familiar)

Position	Code	Description
Pitcher (P)	1	The pitcher not only throws during the defensive inning but also fields. However, pitchers’ batting is not considered in this study.
Catcher (C)	2	Receives pitches and controls defense.
First Base (1B)	3	Handles many throws from other infielders.
Second Base (2B)	4	Defends the right side and middle infield.
Shortstop (SS)	5	Defends the left side and middle infield.
Third Base (3B)	6	Defends left side infield; requires strong arm.
Left Field (LF)	7	Covers left outfield; strong arm needed.
Center Field (CF)	8	Covers middle outfield; requires speed and range.
Right Field (RF)	9	Covers right outfield; also requires strong arm.
Designated Hitter (DH)	-	Only hits, no fielding responsibilities.

II. Research Motivation

(1 min read)

With the rise of sports science and analytics, performance prediction and strategy analysis have become popular in professional baseball. This inspired me to apply R programming to baseball data, combining my academic learning with personal passion for baseball.。

III. Data Processing

(3 min read)

3.1 KPI Function

Before analysis, we define a KPI function to compute players’ age, OBP, SLG, and OPS. Note: For age calculation, players born after July are considered as born in the following year.
Note: For age calculation, players born after July are considered as born in the following year.

KPI function：

KPI <- function(player_id) {
  player_batting <- Batting |> filter(playerID == player_id)
  player_info <- People |> filter(playerID == player_id)

  merged_data <- merge(player_batting, player_info, by = "playerID")

  merged_data |>
    mutate(
      birthyear = if_else(birthMonth >= 7, birthYear + 1, birthYear),
      Age = yearID - birthyear,
      OBP = round((H + BB + HBP) / (AB + BB + HBP + SF), 3),
      SLG = round((H - X2B - X3B - HR + 2 * X2B + 3 * X3B + 4 * HR) / AB, 3),
      OPS = round(SLG + OBP, 3)
    ) |>
    select(Age, OBP, SLG, OPS) 
}

Example with Shohei Ohtani:

KPI("ohtansh01")

3.2 Adding Fielding Position

Next, we define a Position function to add each player’s primary fielding position, so that we can further analyze offensive performance by position.
The logic here is to count the number of appearances at each fielding position in the Appearances table, and then assign the position with the highest count as the player’s main position for that year.

Position <- function(player_id) {
  pos_cols <- c("G_c", "G_1b", "G_2b", "G_3b", 
                "G_ss", "G_lf", "G_cf", "G_rf", "G_dh")
  pos_names <- c("C", "1B", "2B", "3B", 
                 "SS", "LF", "CF", "RF", "DH")
  appearances <- Appearances |> 
  filter(playerID == player_id)
  total_games <- colSums(appearances[pos_cols], na.rm = T)
  main_pos <- pos_names[which.max(total_games)]
  main_pos
}

Again, let’s take Shohei Ohtani as an example to check the position information:

KPI("ohtansh01") |> 
  mutate(Position = Position("ohtansh01"))

Next, we apply the KPI and Position functions to all hitters, excluding players with too few at-bats in a season (e.g., due to injury or pitchers batting).
We then organize the results into one large dataset.

players <- Batting |>  
  filter(AB >= 100) |>
  distinct(playerID) |>
  pull(playerID)

batting_data <- lapply(players, function(pid) {
  kpi_stats <- KPI(pid)                     
  pos       <- Position(pid)            
  kpi_stats |>
    mutate(playerID = pid, Position = pos) |>
    select(playerID, Age, OBP, SLG, OPS, Position)
}) |> 
  bind_rows()

We print the first few rows to check the results:

head(batting_data, 10)

3.3 Adding Basic Player Information

Finally, we add player attributes such as birthplace, height, and weight.

info_data <- People |>
  select(playerID, birthCountry, height, weight) |>
  select(playerID, height, weight)

batting_data <- merge(batting_data, info_data, by = "playerID")

We again print the first few rows to check:

head(batting_data, 10)

(Height and Weight units are inches and pounds, respectively.)

In addition, we extract each player’s peak season (the year with the highest OPS) into a new dataset for further analysis.

batting_topOPS <- batting_data |> 
  group_by(playerID) |> 
  filter(OPS == max(OPS, na.rm = T)) |> 
  slice(1) |>  
  ungroup()

head(batting_topOPS, 10)

3.4 Summary

After this data processing, we now have two datasets:
- batting_data: annual statistics of hitters
- batting_topOPS: only the peak season (highest OPS year) for each hitter

These datasets will be used for subsequent analysis.

batting_data

head(batting_data, 10)

batting_topOPS

head(batting_topOPS, 10)

IV. Analysis Process

(6 min read)

4.1 Relationship Between Age and OPS

4.1.1 Model Assumptions and Testing

First, let’s look at scatterplots of OPS versus Age for several players.
Since Shohei Ohtani is still an active player with relatively few data points, we instead select historically well-known players from different positions for illustration.
(Here we choose: Right Fielder (RF) Hank Aaron, Catcher (C) Mike Piazza, Shortstop (SS) Derek Jeter, and Designated Hitter (DH) Edgar Martinez.)

aaronha = batting_data |> 
          filter(playerID == "aaronha01") |>   
          ggplot() +               
          geom_point(aes(Age, OPS)) +
          scale_x_continuous(limits = c(20, 45)) +
          labs(title = "Hank Aaron (OF)", x = "Age", y = "OPS") +
          theme_bw() +
          theme(plot.title = element_text(hjust = 0.5))

piazzmi = batting_data |> 
            filter(playerID == "piazzmi01") |>   
            ggplot() +               
            geom_point(aes(Age, OPS)) +
            scale_x_continuous(limits = c(20, 45)) +
            labs(title = "Mike Piazza (C)", x = "Age", y = "OPS") +
            theme_bw() +
            theme(plot.title = element_text(hjust = 0.5))

jeterde = batting_data |> 
            filter(playerID == "jeterde01") |>   
            ggplot() +               
            geom_point(aes(Age, OPS)) +
            scale_x_continuous(limits = c(20, 45)) +
            labs(title = "Derek Jeter (SS)", x = "Age", y = "OPS") +
            theme_bw() +
            theme(plot.title = element_text(hjust = 0.5))

martied = batting_data |> 
            filter(playerID == "martied01") |>   
            ggplot() +               
            geom_point(aes(Age, OPS)) +
            scale_x_continuous(limits = c(20, 45)) +
            labs(title = "Edgar Martinez (DH)", x = "Age", y = "OPS") +
            theme_bw() +
            theme(plot.title = element_text(hjust = 0.5))

(aaronha + piazzmi) / (jeterde + martied) + plot_annotation(title = "OPS by Age",
                                            theme = theme(plot.title = element_text(hjust = 0.5, size = 18)))

From the plots, we can see that the peak OPS age differs across positions. For example, Hank Aaron reached his highest OPS at age 37, while Derek Jeter peaked much earlier at age 25.
We can also observe that players’ career trajectories generally form a parabolic shape (similar to a quadratic regression curve). We will now further analyze and test this phenomenon.

Next, we test whether players’ OPS trajectories follow the assumptions of a quadratic regression model:

model <- lm(OPS ~ Age + I(Age^2), batting_data)
model |>  summary()


Call:
lm(formula = OPS ~ Age + I(Age^2), data = batting_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.6840 -0.0824  0.0194  0.1086  4.3184 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  1.404e-01  3.671e-02   3.824 0.000131 ***
Age          3.504e-02  2.531e-03  13.845  < 2e-16 ***
I(Age^2)    -5.648e-04  4.304e-05 -13.123  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2008 on 37257 degrees of freedom
  (24518 observations deleted due to missingness)
Multiple R-squared:  0.006361,  Adjusted R-squared:  0.006308 
F-statistic: 119.3 on 2 and 37257 DF,  p-value: < 2.2e-16

Variable	P-value	Adjusted R²	Interpretation
Age	2e-16 Estimate: 0.035	0.0063	For each additional year of age, OPS increases by about 0.035, indicating a positive relationship between Age and OPS.
I(Age²)	2e-16	0.0063	Quadratic effect: OPS increases first and then decreases, implying the existence of a peak period.

We then examine the residual plots of this model to check whether the assumptions of quadratic regression hold:

model  |> autoplot()

Although the model shows a statistically significant quadratic relationship between Age and OPS, the diagnostic plots reveal skewness and heteroskedasticity in residuals. This indicates prediction errors are not fully random, so interpretation should be cautious.

Next, we draw a quadratic regression curve to visualize the relationship between Age and OPS:

batting_data |> 
  ggplot() +
  geom_smooth(aes(Age, OPS), method  = "lm",formula = y ~ x + I(x^2), size = 1.5) +
  theme_bw() +
  labs(title = "Age vs OPS", x= "Age", y= "OPS") +
  theme(plot.title = element_text(hjust = 0.5, size = 18))

model$coefficients

  (Intercept)           Age      I(Age^2) 
 0.1403716751  0.0350429541 -0.0005647756

a <- model$coefficients["I(Age^2)"]
b <- model$coefficients["Age"]
c <- model$coefficients["(Intercept)"]

vertex_x <- -b / (2 * a)
vertex_y <- a * vertex_x^2 + b * vertex_x + c
print(paste("頂點位置：Age =", round(vertex_x), ", OPS =", round(vertex_y, 3)))

[1] "頂點位置：Age = 31 , OPS = 0.684"

We can see that hitters reach their maximum OPS of about 0.684 at around age 31.

Now let’s further examine how this Age–OPS relationship differs by fielding position:

batting_data |> 
  ggplot() +
  geom_smooth(aes(Age, OPS), method = "lm", formula = y ~ x + I(x^2), size = 1.5) + 
  scale_x_continuous(limits = c(18, 45)) +
  facet_wrap(~ Position, ncol = 3) +
  theme_bw() +
  labs(title = "Age by Fielding Position vs OPS", x = "Age", y = "OPS") +
  theme(plot.title = element_text(hjust = 0.5, size = 18))

From these facet plots, we can see that OPS versus Age follows a parabolic trend across all fielding positions, but the exact peak ages and OPS levels differ by position.
Here, we restrict the x-axis (Age) to 18–45 years to avoid distortion from a few extreme outliers (very young or very old players with few appearances).

4.1.2 Summary

We can see that players across positions reach their peak OPS at different ages, and the peak OPS values also differ.
Next, we will explore whether this variation is related to players’ height and weight.
It is important to note that the quadratic curves above are based on all annual data across all players, so they represent the average OPS by age — not that every player peaks exactly at age 31.
Therefore, in the following analysis, we will switch to the batting_topOPS dataset, which only retains each player’s best OPS season, to study peak ages more directly by position.

4.2 Analysis of Hitters’ Height and Weight

Next, let’s look at the scatter plot of players’ height and weight:

batting_topOPS |> 
  ggplot() + 
  geom_point(aes(weight, height)) +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5, size = 18)) +
  labs(title = "Scatter Plot of MLB Hitters’ Weight and Height", x = "Weight", y = "Height")

We can generally see that players’ heights are concentrated in the range of 6’7”–7’7”, and their weights are mostly within 150–225 lbs.
It is also clear that players can roughly be divided into two categories: taller/heavier type and shorter/lighter type.

Next, let’s examine the scatter plot of height and weight by fielding position:

batting_topOPS |> 
  ggplot() + 
  geom_point(aes(weight, height)) +
  facet_wrap(~ Position) +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5, size = 18)) +
  labs(title = "Scatter Plot of MLB Hitters’ Weight and Height by Fielding Position", x = "Weight", y = "Height")

From the scatterplots, we can see that Designated Hitters (DH) tend to be taller and heavier, while Catchers (C), Second Basemen (2B), and Shortstops (SS) are relatively shorter and lighter.

Scatterplots only provide a general sense of the trend, so next we use sorted boxplots to gain a clearer view:

p_height = batting_topOPS |>
    ggplot() + 
    geom_boxplot(aes(reorder(Position, height, FUN = median), height)) +
    labs(x = NULL)

p_weight = batting_topOPS |>
    ggplot() + 
    geom_boxplot(aes(reorder(Position, weight, FUN = median), weight)) +
    labs(x = "Position")

p_height / p_weight + plot_annotation(title = "Height and Weight Box Plot by Fielding Position",
                                      theme = theme(plot.title = element_text(hjust = 0.5, size = 18,)))

We can observe that Designated Hitters (DH) and First Basemen (1B) have higher medians for both height and weight.
In contrast, positions requiring speed and agility — such as Second Base (2B), Shortstop (SS), Third Base (3B), and Center Field (CF) — have relatively lower median height and weight.

4.3 Peak Age Analysis

4.3.1 Peak Age – Descriptive Analysis

First, let’s look at a table showing the average peak ages (year of highest OPS) by fielding position:

position_summary <- batting_topOPS |>
  group_by(Position) |>
  summarise(avg_Age = round(mean(Age),2)) |>
  arrange(desc(avg_Age))

position_summary

Residual plots by position:

batting_topOPS |> 
  group_by(Position) |> 
  summarise(age0 = mean(Age)) |> 
  mutate(dev   = age0 - mean(age0, na.rm = T),
         hjust = ifelse(dev > 0, 1.07, -0.07)) |> 
  ggplot() +
  geom_col(aes(reorder(Position, dev),dev, 
               fill = dev > 0), show.legend = F) +
  geom_text(
    aes(x = reorder(Position, dev), y = dev, label = round(dev, 2), hjust = hjust),
    vjust = 0.4,
    size  = 3.3,
    color = "white",
    fontface  = "bold",
  ) +
  coord_flip() +
  scale_fill_manual(values = c("FALSE" = "red2", "TRUE" = "black")) +
  labs(title = "Max-OPS Age Deviation by Position", x = "Fielding Position", y = "Deviation from Mean Age at Max OPS") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5, size = 18)
        ,axis.text.y = element_text(size = 10))

We can see that the four positions with the latest average peak ages are Designated Hitter (DH), Catcher (C), First Base (1B), and Left Field (LF), though the actual differences are quite small.

Next, let’s examine a heatmap of Height, Weight, and Age:

xbk = batting_topOPS %$% seq(min(weight, na.rm = T), max(weight, na.rm = T), length = 10)
xbk1 = round(xbk[-1] - diff(xbk)[1]/2, 1)

ybk = batting_topOPS %$% seq(min(height, na.rm = T), max(height, na.rm = T), length = 10)
ybk1 = round(ybk[-1] - diff(ybk)[1]/2, 1)


batting_topOPS |> 
  mutate(
    weight_bin = cut(weight, breaks = xbk, labels = xbk1, include.lowest = T),
    height_bin = cut(height, breaks = ybk, labels = ybk1, include.lowest = T)
  ) |> 
  group_by(weight_bin, height_bin) |> 
  summarise(kpi = mean(Age, na.rm = T)) |> ungroup() |>
  complete(weight_bin, height_bin, fill = list(kpi = NA)) |> 
  ggplot(aes(weight_bin, height_bin)) +
  geom_tile(aes(fill = kpi)) +
  geom_text(aes(label = round(kpi, 1)), color = "white", size = 4, hjust = 0.5) +
  scale_fill_gradient(low = "gray", high = "#000" , na.value = "white") +
  labs(title = "Max-OPS Avg Age by Weight and Height Combination in MLB Hitters", x = "Weight", y = "Height", fill = "Max-OPS Avg Age") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 1, size = 18),
        axis.text.x = element_text(hjust = 1),
        legend.title = element_text(hjust = 0.5) )

It can be observed that height and weight do not show a clear relationship with peak age.

4.3.2 Peak Age – Regression Analysis

We then run a regression analysis of peak age against height and weight to test for statistical significance.

model_Age <- lm(Age ~ height + weight, batting_topOPS)
model_Age |> summary()


Call:
lm(formula = Age ~ height + weight, data = batting_topOPS)

Residuals:
    Min      1Q  Median      3Q     Max 
-8.9927 -2.5318 -0.4767  2.1320 14.9971 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 29.250505   2.050601  14.264  < 2e-16 ***
height       0.010230   0.032136   0.318     0.75    
weight      -0.014757   0.003178  -4.643 3.54e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.642 on 4251 degrees of freedom
Multiple R-squared:  0.006819,  Adjusted R-squared:  0.006352 
F-statistic: 14.59 on 2 and 4251 DF,  p-value: 4.828e-07

Variable	P-value		Adjusted R²	Interpretation
Variable	Height	Weight	Adjusted R²	Interpretation
Age	0.75	3.54e-06	0.006352	Only weight shows a significant effect on peak age, but the overall explanatory power of the model is still very weak.

We also validate the regression assumptions for the model of peak age against height and weight:

model_Age  |> autoplot()

Overall, the assumptions hold reasonably well, with no severe violations of linear regression requirements.

4.4 Peak OPS Analysis

4.4.1 Peak OPS – Descriptive Analysis

First, let’s look at a table showing the average peak OPS (the highest OPS season) by fielding position:

OPS_summary <- batting_topOPS |>
  group_by(Position) |>
  summarise(avg_OPS = round(mean(OPS),3)) |>
  arrange(desc(avg_OPS))

OPS_summary

Next, we examine the residual plot of peak OPS by position:

batting_topOPS |> 
  group_by(Position) |> 
  summarise(OPS0 = mean(OPS)) |> 
  mutate(dev   = OPS0 - mean(OPS0, na.rm = T),
         hjust = ifelse(dev > 0, 1.0, -0.07)) |> 
  ggplot() +
  geom_col(aes(reorder(Position, dev),dev, 
               fill = dev > 0), show.legend = F) +
  geom_text(
    aes(x = reorder(Position, dev), y = dev, label = round(dev, 2), hjust = hjust),
    vjust = 0.4,
    size  = 3,
    color = "white",
    fontface  = "bold",
  ) +
  coord_flip() +
  scale_fill_manual(values = c("FALSE" = "red2", "TRUE" = "black")) +
  labs(title = "Max-OPS Age Deviation by Position", x = "Fielding Position", y = "Deviation from Mean OPS at Max OPS") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5, size = 18),
        axis.text.y = element_text(size = 10))

We can see that the top two positions in peak OPS are Designated Hitter (DH) and First Base (1B), while the lowest two are Shortstop (SS) and Second Base (2B).

Next, let’s explore the heatmap of players’ Height, Weight, and OPS:

batting_topOPS |> 
  mutate(
    weight_bin = cut(weight, breaks = xbk, labels = xbk1, include.lowest = T),
    height_bin = cut(height, breaks = ybk, labels = ybk1, include.lowest = T)
  ) |> 
  group_by(weight_bin, height_bin) |> 
  summarise(kpi = mean(OPS, na.rm = T)) |> ungroup() |>
  complete(weight_bin, height_bin, fill = list(kpi = NA)) |> 
  ggplot(aes(weight_bin, height_bin)) +
  geom_tile(aes(fill = kpi)) +
  geom_text(aes(label = round(kpi, 3)), color = "white", size = 4) +
  scale_fill_gradient(low = "gray", high = "#000" , na.value = "white") +
  labs(title = "Max-OPS Age Avg OPS by Weight and Height Combination in MLB Hitters",x = "Weight", y = "Height", fill = "Max-OPS Age Avg OPS") +
  theme_bw() +
  theme(plot.title = element_text(hjust = -1, size = 18),
        axis.text.x = element_text(hjust = 1),
        legend.title = element_text(hjust = 0.5) )

Compared with the peak age analysis, the OPS heatmap reveals a clearer trend: taller and heavier players tend to have higher OPS.
Designated Hitters (DH) and First Basemen (1B) are generally taller and heavier, which matches the residual plot where they also showed higher peak OPS values.

After noticing this interesting pattern, we further investigate which component of OPS — On-base Percentage (OBP) or Slugging Percentage (SLG) — contributes more to this difference.
Below are the heatmaps for OBP and SLG:

OBP_plot = batting_topOPS |> 
  mutate(
    weight_bin = cut(weight, breaks = xbk, labels = xbk1, include.lowest = T),
    height_bin = cut(height, breaks = ybk, labels = ybk1, include.lowest = T)
  ) |> 
  group_by(weight_bin, height_bin) |> 
  summarise(kpi = mean(OBP, na.rm = T)) |> ungroup() |>
  complete(weight_bin, height_bin, fill = list(kpi = NA)) |> 
  ggplot(aes(weight_bin, height_bin)) +
  geom_tile(aes(fill = kpi)) +
  geom_text(aes(label = round(kpi, 3)), color = "white", size = 3.5) +
  scale_fill_gradient(low = "gray", high = "#000" , na.value = "white") +
  ggtitle("OBP") +
  labs(x = "Weight", y = "Height", fill = "Max-OPS Age Avg OBP") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5, size = 14),
        axis.text.x = element_text(hjust = 1),
        legend.title = element_text(hjust = 0.5) )

SLG_plot = batting_topOPS |> 
  mutate(
    weight_bin = cut(weight, breaks = xbk, labels = xbk1, include.lowest = T),
    height_bin = cut(height, breaks = ybk, labels = ybk1, include.lowest = T)
  ) |> 
  group_by(weight_bin, height_bin) |> 
  summarise(kpi = mean(SLG, na.rm = T)) |> ungroup() |>
  complete(weight_bin, height_bin, fill = list(kpi = NA)) |> 
  ggplot(aes(weight_bin, height_bin)) +
  geom_tile(aes(fill = kpi)) +
  geom_text(aes(label = round(kpi, 3)), color = "white", size = 3.5) +
  scale_fill_gradient(low = "gray", high = "#000" , na.value = "white") +
  ggtitle("SLG") +
  labs(x = "Weight", y = "Height", fill = "Max-OPS Age Avg SLG") +
  theme_bw() +
  theme(plot.title = element_text(hjust = 0.5, size = 14),
        axis.text.x = element_text(hjust = 1),
        legend.title = element_text(hjust = 0.5) )

OBP_plot / SLG_plot + plot_annotation(title = "Max-OPS Age Avg OBP and SLG by Weight and Height Combination in MLB Hitters",
                                      theme = theme(plot.title = element_text(hjust = 0.5, size = 18)))

We can see that larger (taller/heavier) hitters show a noticeably stronger effect on SLG, while OBP does not show significant differences.

4.4.2 Peak OPS – Regression Analysis

We then run regression analyses of peak OPS against height and weight to verify the relationship.

OPS:

model_OPS <- lm(OPS ~ height + weight, batting_topOPS)
model_OPS |> summary()


Call:
lm(formula = OPS ~ height + weight, data = batting_topOPS)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.8663 -0.1192 -0.0321  0.0606  4.1279 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 0.2083722  0.1351950   1.541  0.12333    
height      0.0058123  0.0021187   2.743  0.00611 ** 
weight      0.0011682  0.0002096   5.575 2.63e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.2401 on 4251 degrees of freedom
Multiple R-squared:  0.01879,   Adjusted R-squared:  0.01832 
F-statistic: 40.69 on 2 and 4251 DF,  p-value: < 2.2e-16

OBP:

model_OPS_OBP <- lm(OBP ~ height + weight, batting_topOPS)
model_OPS_OBP |> summary()


Call:
lm(formula = OBP ~ height + weight, data = batting_topOPS)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.37018 -0.04483 -0.01229  0.02403  0.63432 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  3.258e-01  5.166e-02   6.307 3.14e-10 ***
height       6.555e-04  8.095e-04   0.810    0.418    
weight      -2.105e-05  8.007e-05  -0.263    0.793    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.09175 on 4251 degrees of freedom
Multiple R-squared:  0.0001668, Adjusted R-squared:  -0.0003036 
F-statistic: 0.3546 on 2 and 4251 DF,  p-value: 0.7015

SLG:

model_OPS_SLG <- lm(SLG ~ height + weight, batting_topOPS)
model_OPS_SLG |> summary()


Call:
lm(formula = SLG ~ height + weight, data = batting_topOPS)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.5020 -0.0857 -0.0239  0.0430  3.4995 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.1174070  0.0977304  -1.201 0.229688    
height       0.0051568  0.0015316   3.367 0.000767 ***
weight       0.0011892  0.0001515   7.851  5.2e-15 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.1736 on 4251 degrees of freedom
Multiple R-squared:  0.03404,   Adjusted R-squared:  0.03358 
F-statistic:  74.9 on 2 and 4251 DF,  p-value: < 2.2e-16

Variable	P-value		Adjusted R²	Interpretation
Variable	Height	Weight	Adjusted R²	Interpretation
OPS	0.0061	2.63e-08	0.0183	Both height and weight have significant effects on OPS, but the overall explanatory power remains weak.
OBP	0.418	0.793	-0.0003	No significance for either variable; predictive power is essentially zero.
SLG	0.00077	5.2e-15	0.0336	Both variables are significant, but the predictive power is still weak.

We also validate the regression assumptions for the OPS model against height and weight:

model_OPS  |> autoplot()

Overall, the model does not show major violations of the basic assumptions of linear regression.

V. Conclusion

(2 min read)

5.1 Relationship Between Peak Age, Peak OPS, and Height/Weight

Below is a summary table of the main findings:

Analysis Item	Result	Explanation
Peak Age	Average ~28.5 years	The differences in peak age across positions are small, with an overall average around 28.5 years.
Peak OPS	Average ~0.85	The differences in peak OPS across positions are larger. The top two are Designated Hitter (DH) and First Base (1B), while the bottom two are Shortstop (SS) and Second Base (2B).
Impact of Height/Weight on Peak Age	Height: not significant; Weight: slight negative effect	Height does not significantly affect peak age, but heavier players tend to peak slightly earlier.
Impact of Height/Weight on Peak OPS	Both positively correlated	Height and weight are significantly positively related to peak OPS. However, the effect is primarily driven by Slugging Percentage (SLG) rather than On-base Percentage (OBP).

5.2 Players Shift Fielding Positions During Their Careers

Although the batting_topOPS dataset shows that peak ages are not significantly different across positions, the earlier Age–OPS plots using batting_data reveal that players at less defensively demanding positions such as Designated Hitter (DH) and First Base (1B) tend to reach their OPS peak later.
This difference likely occurs because star hitters (whose OPS is consistently above average) often transition to DH or 1B in the later stages of their careers. This raises the OPS-age curve for those positions, making their peak age appear later.
For example, an outfielder who declines defensively but retains strong offensive ability is often moved to DH or 1B to extend his career. As a result, these positions include more older players who still maintain high OPS, causing the estimated peak age from batting_data to shift upward compared with other positions.

Analysis of Peak Offensive Age in MLB Hitters

(15 min read)

Wu Cheng-Yen

I. Abstract and Research Topic Introduction

1.1Research Topic Introduction:

1.2 Database Introduction:

Batting

Appearances

1.3 Metrics:

1.4 Fielding Position Introduction:

II. Research Motivation

III. Data Processing

3.1 KPI Function

3.2 Adding Fielding Position

3.3 Adding Basic Player Information

3.4 Summary

batting_data

batting_topOPS

IV. Analysis Process

4.1 Relationship Between Age and OPS

4.1.1 Model Assumptions and Testing

4.1.2 Summary

4.2 Analysis of Hitters’ Height and Weight

4.3 Peak Age Analysis

4.3.1 Peak Age – Descriptive Analysis

4.3.2 Peak Age – Regression Analysis

4.4 Peak OPS Analysis

4.4.1 Peak OPS – Descriptive Analysis

4.4.2 Peak OPS – Regression Analysis

V. Conclusion

5.1 Relationship Between Peak Age, Peak OPS, and Height/Weight

5.2 Players Shift Fielding Positions During Their Careers